Question

What concentrations of \[FC{{H}_{2}}COOH\text{ }\left( {{K}_{a}}=2.6\times {{10}^{-3}} \right)\]is needed so that \[\left[ {{H}^{+}} \right]=2\times {{10}^{-3}}:\]
A.$1.53\times {{10}^{-3}}M.$
B.$2.60\times {{10}^{-3}}M.$
C.$5.20\times {{10}^{-3}}M.$
D.$3.53\times {{10}^{-3}}M.$

Answer 1

Hint: We know that the fluoroacetic acid is a weak acid and for ionization if feebly possible, it means we have to apply the Ostwald law of dilution of weak electrolytes and the value of both concentration as well as for dissociation constant in the Ostwald law and calculate the concentration of \[FC{{H}_{2}}COOH.\]

Complete answer:
As we know, the ionization degree of acids and bases depends on the degree of dissociation of compounds into their constituent ions. The strong acids and bases have a high degree of ionization when compared to the ionization of weak acid and base. Also, a strong acid implies a good proton donor, whereas a strong base implies a good proton acceptor for example, dissociation of weak acid. All these acids are referred to as strong acids. Ionization of acids produces hydrogen ions, and therefore, these compounds act as proton donors.
In the same way, a few bases such as sodium hydroxide (NaOH), lithium hydroxide (LiOH) dissociate completely into their ions in an aqueous solution or medium. These bases are referred to as strong bases. The ionization of these bases produces hydroxyl ions. The acid dissociation constant is measured by dividing the concentration of individual cation and anion formed by dissociation of acid by the concentration of acid. Here as we know that the $\alpha =\sqrt{\dfrac{{{K}_{a}}}{C}}$ where $\left[ {{H}^{+}} \right]=C\alpha =\sqrt{C\times {{K}_{a}}}=2\times {{10}^{-3}}.$ Now by substituting the values we get the value of C;
$C=2\times {{10}^{-3}}M$ and $Ka=2.6\times {{10}^{-3}}$ $\Rightarrow C=\dfrac{{{\left( 2\times {{10}^{-3}} \right)}^{2}}}{2.6\times {{10}^{-3}}}=1.53\times {{10}^{-3}}.$

Therefore, the correct answer is option A.

Note:
Remember that the equilibrium constant for the ionization of an acid describes its Acid Ionization Constant (Ka). However, the stronger the acid, the acid ionization constant (Ka) will be larger. It means that a strong acid is a donor of a better proton.